Four years ago at this time, Michael Bloomberg was practically begging the political world to treat him as a potential presidential candidate.

He made a show of leaving the Republican Party and registering as an independent, while his right-hand man, Kevin Sheekey, launched one trial balloon after another about a potential third party bid. But when it became clear that the two major parties would nominate Barack Obama and John McCain — both of whom enjoyed significant popularity with independents — whatever opening might have existed for Bloomberg slammed shut and the mayor backed down.

This time around, Bloomberg is being far more subdued, repeatedly insisting he has no interest in running. And when he was asked on “Good Morning America” earlier this week whether an independent candidate — even one not named Bloomberg — might be able to run a serious race in 2012, his reply was blunt: “No. The deck is stacked for — one of the two major party candidates will be elected.”

So that settles that, right?

Well, maybe. And maybe not. Because there’s a big difference between the 2012 and 2008 elections: This time around, Bloomberg won’t need to ask for attention to get it.

In the modern era of politics, two conditions must be met for there to be room (at least potentially) for a credible independent presidential candidacy. The first is that there needs to be an unpopular incumbent whose standing is weighted down by a broad sense of popular anxiety. The second is that the opposition party needs to field a candidate whose own liabilities make it difficult for him or her to capitalize on voters’ eagerness to toss out the incumbent.

These conditions were present back in 1980, when double-digit unemployment and inflation had the public itching to get rid of Jimmy Carter. But GOP nominee Ronald Reagan was (at the time) widely regarded as a trigger-happy conservative ideologue, creating an opening for John Anderson, a liberal Republican congressman, to enter the race as an independent. Reagan ended up winning over most of the doubters and winning easily, but in the spring of 1980, Anderson ran at over 20% in national polls.

The same conditions applied in 1992, when a rotten economy soured voters on George H.W. Bush — even as a series of personal scandals kept them from flocking to Bill Clinton. Enter Ross Perot, who rocketed to nearly 40% in polls by the middle of ’92, briefly taking the lead before cracking up and dropping out. Even after that circus, Perot was still able to return to the race a month before the election and wind up with 19% of the vote.

And now, for the first time since ’92, it’s looking like those two magic conditions will again be present in 2012.

President Obama’s approval rating long ago slipped into the danger zone, and all of the recent evidence suggests there’ll be no economic miracle between now and November 2012. The public, in other words, will probably be in a firing mood.

But the GOP doesn’t exactly have its act together. The party’s most likely nominee is probably Mitt Romney, and the best thing that can be said about him is that he’s not any of the other Republican candidates. And if Romney’s not the candidate, it will almost certainly be either Texas Gov. Rick Perry or Minnesota Rep. Michele Bachmann — both of whom have the potential to make swing voters very skittish.

And then there’s the party’s own profound image problem. A poll released this week shows that just 33% of Americans have a favorable view of the GOP — the party’s worst-ever mark, and a figure that’s 14 points lower than the Democrats’ number. Voters, it seems, will need a lot of convincing to hand the keys to the Republicans, even if they do want Obama out.

So the recipe that made Anderson and Perot credible players is likely to exist again. Which means that in the months ahead we’re only going to hear more and more from the media and the political class about the unusual opening that exists for a serious, well-funded independent candidate. And there’s no better known serious, well-funded independent politician in America than Michael Bloomberg. As the ’12 race comes into focus, it won’t take many winks to get the press speculating about a potential Bloomberg bid.

The big question is what Bloomberg, deep inside, makes of all of this. Obviously, he relishes the attention, and — especially as the media’s speculation mounts — he’ll surely have more than a few people whispering in his ear that the time is right to go national. And at 69 years old (70 next February), this is surely his last chance to take a shot.

Of course, Bloomberg is also a realist, and he’s almost certainly right that — at the end of the day — an independent has no actual chance of winning in 2012. Here’s betting that that knowledge will ultimately keep him on the sidelines — but not after an extended, months-long dance.